Theories of fiber packing, of use in manufacturing composite materials, are developed. The maximum packing fraction of force free fibers is estimated based on a statistical analysis of the distribution of fiber-fiber contact points. The new expressions are more general than previous ones by allowing for a distribution in fiber length and orientation. The forced packing beyond this limit is governed by the bending of fiber segments between contact points. A micromechanical theory is developed for this, again based on the contact point statistics, and equations relating the force response per unit area of a fiber bed to the fiber volume fraction are derived for three basic types of assembly : a general 3D wad, a planar mat of dispersed fibers, and a bundle of almost parallel fibers. Other types of reinforcement structure, such as woven fabrics, and the effect of lubrication are also treated briefly.